Pith Number

pith:VPG7CYAE

pith:2016:VPG7CYAELVKNSLZWV2C3TFIX5D

not attested not anchored not stored refs pending

Optimal Boundary Estimates for Stokes Systems in Homogenization Theory

Qiang Xu, Shu Gu

arxiv:1612.06042 v1 · 2016-12-19 · math.AP

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{VPG7CYAELVKNSLZWV2C3TFIX5D}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T00:54:46.046105Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

abcdf160045d54d92f36ae85b99517e8f1c4f7fdc46c5815be1ea387ab8d787f

Aliases

arxiv: 1612.06042 · arxiv_version: 1612.06042v1 · doi: 10.48550/arxiv.1612.06042 · pith_short_12: VPG7CYAELVKN · pith_short_16: VPG7CYAELVKNSLZW · pith_short_8: VPG7CYAE

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/VPG7CYAELVKNSLZWV2C3TFIX5D \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: abcdf160045d54d92f36ae85b99517e8f1c4f7fdc46c5815be1ea387ab8d787f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "78e7fb2431805908bab8bd2f97fb30e900b632051a6e1c6e17c2c8432a20cc84",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.AP",
    "submitted_at": "2016-12-19T04:15:48Z",
    "title_canon_sha256": "73de54f34256fc25e4c9a7db72ff7caf0a9f964bb64dafd041372346e373da97"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1612.06042",
    "kind": "arxiv",
    "version": 1
  }
}